Multivariate Inverse Gaussian Distribution Research Articles

Adaptive target detection against spatially correlated compound‐Gaussian clutter with multivariate inverse Gaussian texture

To improve the detection performance in the presence of target-steering vector mismatches, a novel robust adaptive matched filter (AMF) detector for compound Gaussian clutter is proposed. First, the multivariate inverse Gaussian distribution is first introduced to compound Gaussian clutter model. Second, the texture value is estimated with maximum a posteriori (MAP) estimator in spatial domain, which has a closed form and is not affected by the target's steering vector mismatch. A robust AMF detector is derived based on this estimation. Simulation results demonstrate that the proposed detector can achieve better performance in the presence of target-steering vector mismatches.

A THEORETICAL ANALYSIS OF MULTISCALE ENTROPY UNDER THE INVERSE GAUSSIAN DISTRIBUTION

Multiscale entropy (MSE) discloses the intrinsic multiple scales in the complexity of physical and physiological signals, which are usually featured by heavy-tailed distributions. Most of these research results are pure experimental search, till Costa et al. made the first attempt to the theoretical basis of MSE. However, the analysis only supports the Gaussian distribution [Phys. Rev. E71, 021906 (2005)]. In this paper, we present the theoretical basis of MSE under the inverse Gaussian distribution, which is a typical model for physiological, physical and financial data sets. The analysis is applicable to uncorrelated inverse Gaussian process and 1/f noise with the multivariate inverse Gaussian distribution, providing a reliable foundation for potential applications of MSE to explore complex physical and physiological time series.

Multiscale Entropy under the Inverse Gaussian Distribution:Analytical Results

The multiscale entropy (MSE) reveals the intrinsic multiple scalesin the complexity of physical and physiological signals, which areusually featured by heavy-tailed distributions. However, most researchresults are pure experimental search. Recently, Costa et al. have madethe first attempt to present the theoretical basis of MSE, but it onlysupports the Gaussian distribution [Phys Rev. E 71 (2005)021906]. We present the theoretical basis of MSE under theinverse Gaussian distribution, a typical model for physiological,physical and financial data sets. The analysis allows for uncorrelatedinverse Gaussian process and 1/f noise with the multivariateinverse Gaussian distribution, and then provides a reliable foundationfor the potential applications of MSE to explore complex physical andphysical time series.

Multivariate inverse Gaussian distribution as a limit of multivariate waiting time distributions

Multivariate inverse Gaussian distribution proposed by Minami [2003. A multivariate extension of inverse Gaussian distribution derived from inverse relationship. Commun. Statist. Theory Methods 32(12), 2285–2304] was derived through multivariate inverse relationship with multivariate Gaussian distributions and characterized as the distribution of the location at a certain stopping time of a multivariate Brownian motion. In this paper, we show that the multivariate inverse Gaussian distribution is also a limiting distribution of multivariate Lagrange distributions, which is a family of waiting time distributions, under certain conditions.

A Multivariate Extension of Inverse Gaussian Distribution Derived from Inverse Relationship

We propose a new multivariate extension of the inverse Gaussian distribution derived from a certain multivariate inverse relationship. First we define a multivariate extension of the inverse relationship between two sets of multivariate distributions, then define a reduced inverse relationship between two multivariate distributions. We derive the multivariate continuous distribution that has the reduced multivariate inverse relationship with a multivariate normal distribution and call it a multivariate inverse Gaussian distribution. This distribution is also characterized as the distribution of the location of a multivariate Brownian motion at some stopping time. The marginal distribution in one direction is the inverse Gaussian distribution, and the conditional distribution in the space perpendicular to this direction is a multivariate normal distribution. Mean, variance, and higher order cumulants are derived from the multivariate inverse relationship with a multivariate normal distribution. Other properties such as reproductivity and infinite divisibility are also given.

Bivariate inverse gaussian distribution

A bivariate inverse Gaussian (IG) density function is constructed. Relations of the bivariate IG distribution to the normal and χ2 distributions are established. The corresponding bivariate random walk (RW) density function is obtained. The properties and behaviour of bivariate IG distribution are studied for large parametric values. Moment estimates of the five parameters are given and applications are pointed out. A generalization to the multivariate IG distribution is proposed.